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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 135252o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 135252.t2 | 135252o1 | \([0, 0, 0, -409224, -91475147]\) | \(26919436288/2738853\) | \(771098330122116048\) | \([2]\) | \(1990656\) | \(2.1680\) | \(\Gamma_0(N)\)-optimal |
| 135252.t1 | 135252o2 | \([0, 0, 0, -6378519, -6200451650]\) | \(6371214852688/77571\) | \(349430180098910976\) | \([2]\) | \(3981312\) | \(2.5146\) |
Rank
sage: E.rank()
The elliptic curves in class 135252o have rank \(1\).
Complex multiplication
The elliptic curves in class 135252o do not have complex multiplication.Modular form 135252.2.a.o
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
